On the Stability of an Electrostatically-Actuated Functionally Graded Magneto-Electro-Elastic Micro-Beams Under Magneto-Electric Conditions

Document Type: Research Paper

Authors

Mechanical Engineering Department, Urmia University, Urmia, Iran

Abstract

In this paper, the stability of a functionally graded magneto-electro-elastic (FG-MEE) micro-beam under actuation of electrostatic pressure is studied. For this purpose Euler-Bernoulli beam theory and constitutive relations for magneto-electro-elastic (MEE) materials have been used. We have supposed that material properties vary exponentially along the thickness direction of the micro-beam. Governing motion equations of the micro-beam are derived by using of Hamilton’s principle. Maxwell’s equation and magneto-electric boundary conditions are used in order to determine and formulate magnetic and electric potentials distribution along the thickness direction of the micro-beam. By using of magneto-electric potential distribution, effective axial forces induced by external magneto-electric potential are formulated and then the governing motion equation of the micro-beam under electrostatic actuation is obtained. A Galerkin-based step by step linearization method (SSLM) has been used for static analysis. For dynamic analysis, the Galerkin reduced order model has been used. Static pull-in instability for 5 types of MEE micro-beam with different gradient indexes has been investigated. Furthermore, the effects of external magneto-electric potential on the static and dynamic stability of the micro-beam are discussed in    detail.

Keywords

[1] Davi G., Milazzo A., 2011, A regular variational boundary model for free vibrations of magneto-electro-elastic structures, Engineering Analysis with Boundary Elements 35: 303-312.
[2] Fakhzan M.N., Muthalif Asan G.A., 2013, Harvesting vibration energy using piezoelectric material: Modeling, simulation and experimental verifications, Mechatronics 23: 61-66.
[3] Amiri A., Fakhari S.M., Pournaki I.J., Rezazadeh G., Shabani R., 2015, Vibration analysis of circular magneto-electro-elastic Nano-plates based on Eringen's nonlocal theory, International Journal of Engineering, Transactions C: Aspects 28(12): 1808-1817.
[4] Liu C., Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2013, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures 106: 167-174.
[5] Daga A., Ganesan N., Shankar K., 2009, Behavior of magneto-electro-elastic sensors under transient mechanical loading, Sensors and Actuators A: Physical 150: 46-55.
[6] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory, Composite Structures 111: 522-529.
[7] Linnemann K., Klinkel S., Wagner W., 2009, A constitutive model for magnetostrictive and piezoelectric materials, International Journal of Solids and Structures 46: 1149-1166.
[8] Xue C.X., Pan E., Zhang S.Y., 2011, Large deflection of a rectangular magnetoelectroelastic thin plate, Mechanics Research Communications 38: 518-523.
[9] Pan E., Heyliger P.R., 2003, Exact solutions for magneto-electro-elastic laminates in cylindrical bending, International Journal of Solids and Structures 40: 6859-6876.
[10] Ke L.L., Wang Y.S., 2014, Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E 63: 52-61.
[11] Amiri A., Pournaki I.J., Jafarzadeh E., Shabani R., Rezazadeh G., 2016, Vibration and instability of fluid-conveyed smart micro-tubes based on magneto-electro-elasticity beam model, Microfluidics and Nanofluidics 20(2): 1-10.
[12] Liu M.F., 2011, An exact deformation analysis for the magneto-electro-elastic fiber-reinforced thin plate, Applied Mathematical Modelling 35: 2443-2461.
[13] Huang D.J., Ding H.J., Chen W.Q., 2007, Analytical solution for functionally graded magneto-electro-elastic plane beams, International Journal of Engineering Science 45: 467-485.
[14] Chang T.P., 2013, On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid, Applied Mathematical Modelling 37: 2503-2515.
[15] Alaimo A., Milazzo A., Orlando C., 2013, A four-node MITC finite element for magneto-electro-elastic multilayered plates, Computers and Structures 129: 120-133.
[16] Li Y.S., 2014, Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation, Mechanics Research Communications 56: 104-114.
[17] Chang T.P., 2013, Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates, Computers and Fluids 84: 247-254.
[18] Zhou Z.G., Wang B., Sun Y.G., 2004, Two collinear interface cracks in magneto-electro-elastic composites, International Journal of Engineering Science 42: 1155-1167.
[19] Li J.Y., 2000, Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials, International Journal of Engineering Science 38: 1993-2011.
[20] Milazzo A., 2014, Large deflection of magneto-electro-elastic laminated plates, Applied Mathematical Modelling 38: 1737-1752.
[21] Xue C.X., Pan E., 2013, On the longitudinal wave along a functionally graded magneto-electro-elastic rod, International Journal of Engineering Science 62: 48-55.
[22] Raeisifard H., Bahrami M.N., Yousefi-Koma A., Raeisi Fard H., 2014, Static characterization and pull-in voltage of a micro-switch under both electrostatic and piezoelectric excitations, European Journal of Mechanics A/Solids 44: 116-124.
[23] Mobki H., Sadeghi M.H., Rezazadeh G., Fathalilou M., Keyvani-janbahan A.A., 2014, Nonlinear behavior of a nano-scale beam considering length scale-parameter, Applied Mathematical Modelling 38: 1881-1895.
[24] Rezazadeh G., Madinei H., Shabani R., 2012, Study of parametric oscillation of an electrostatically actuated microbeam using variational iteration method, Applied Mathematical Modelling 36: 430-443.
[25] Zhang W.M., Yan H., Peng Z.K., Meng G., 2014, Electrostatic pull-in instability in MEMS/NEMS: A review, Sensors and Actuators A: Physical 214: 187-218.
[26] Khanchehgardan A., Rezazadeh G., Shabani R., 2014, Effect of mass diffusion on the damping ratio in micro-beam resonators, International Journal of Solids and Structures 51: 3147-3155.
[27] Khanchehgardan A., Shah-Mohammadi-Azar A., Rezazadeh G., Shabani R., 2013, Thermo-elastic damping in nano-beam resonators based on nonlocal theory, International Journal of Engineering 26(12): 1505-1514.
[28] Duan J.S., Rach R., 2013, A pull-in parameter analysis for the cantilever NEMS actuator model including surface energy, fringing field and Casimir effects, International Journal of Solid and Structures 50: 3511-3518.
[29] Taghavi N., Nahavi H., 2013, Pull-in instability of cantilever and fixed-fixed nano-switches, European Journal of Mechanics A/Solids 41: 123-133.
[30] Wang K.F., Wang B.L., 2014, Influence of surface energy on the non-linear pull-in instability of nano-switches, International Journal of Non-linear Mechanics 59: 69-75.
[31] Yu Y.P., Wu B.S., 2014, An approach to predicting static responses of electrostatically actuated micro-beam under the effect of fringing field and Casimir force, International Journal of Mechanical Science 80: 183-192.
[32] Zamanzadeh M., Rezazadeh G., Jafarsadeghi-poornaki I., Shabani R., 2013, Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes, Applied Mathematical Modelling 37: 6964-6978.
[33] Mobki H., Rezazadeh G., Sadeghi M., Vakili-Tahami F., Seyyed-Fakhrabadi M.S., 2013, A comprehensive study of stability in an electro-statically actuated micro-beam, International Journal of Non-linear Mechanics 48: 78-85.
[34] Osterberg P.M., Senturia S.D., 1997, M-test: A test chip for MEMS material property measurement using electrostatically actuated test structure, Journal of Microelectromechanical Systems 6 (2): 107-118.